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  • Atmospheric Dynamics

    Mankin Mak Atmospheric Dynamics

    M ak Atm

    ospheric Dynam ics

    Mankin Mak

    Atmospheric dynamics is a core component of all atmospheric science curricula. It is concerned with how and why different classes of geophysical disturbances form, what dictates their structure and movement, how the Earth’s uneven surface impacts with them, how they evolve to mature stage, how they interact with the background flow, how they decay and how they collectively constrain the general circulation of the atmosphere.

    Mankin Mak’s new textbook provides a self-contained course on atmospheric dynamics. The first half of the book is suitable for undergraduates, and develops the physical, dynamical and mathematical concepts at the fundamental level. The second half of the book is aimed at more advanced students who are already familiar with the basics. The contents have been developed from many years of the author’s teaching at the University of Illinois. The discussions are supplemented with schematics, weather maps and statistical plots of the atmospheric general circulation. Students often find the connection between theoretical dynamics and atmospheric observation somewhat tenuous, and this book demonstrates a strong connection between the key dynamics and real observations in the atmosphere, with many illustrative analyses in the simplest possible model settings. Physical reasoning is shown to be even more crucial than mathematical skill in tackling dynamical problems.

    This textbook is an invaluable asset for courses in atmospheric dynamics for undergraduates as well as graduate students and researchers in atmospheric science, ocean science, weather forecasting, environmental science and applied mathematics. Some background in mathematics and physics is assumed.

    Cover illustration:

    © Science Photo Library.

    Cover designed by Hart McLeod Ltd

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    Atmospheric Dynamics

    Atmospheric dynamics is a core component of all atmospheric science curricula. It is concerned with how and why different classes of geophysical disturbances form, what dictates their structure and movement, how the Earth's uneven surface impacts with them, how they evolve to mature stage, how they interact with the background flow, how they decay and how they collectively constrain the general circulation of the atmosphere.

    Mankin Mak’s new textbook provides a self-contained course on atmospheric dynamics. The first half of the book is suitable for undergraduates, and develops the physical, dynamical and mathematical concepts at the fundamental level. The second half of the book is aimed at more advanced students who are already familiar with the basics. The contents have been developed from many years of the author’s teaching at the University of Illinois. The discussions are supplemented with schematics, weather maps and statistical plots of the atmospheric general circulation. Students often find the connection between theoretical dynamics and atmospheric observation somewhat tenuous, and this book demonstrates a strong connection between the key dynamics and real observations in the atmosphere, with many illustrative analyses in the simplest possible model settings. Physical reasoning is shown to be even more crucial than mathematical skill in tackling dynamical problems.

    This textbook is an invaluable asset for courses in atmospheric dynamics for under- graduates as well as graduate students and researchers in atmospheric science, ocean science, weather forecasting, environmental science and applied mathematics. Some back- ground in mathematics and physics is assumed.

    Mankin Mak is a Professor Emeritus in the Department of Atmospheric Sciences at the University of Illinois at Urbana Champaign, where he has taught and researched on atmospheric dynamics for many years. He was born in Hong Kong, China, where he completed his high school education, before moving on to undergraduate study in Engin- eering Physics at the University of Toronto, Canada, and graduate study in Meteorology at the Massachusetts Institute of Technology, USA. He has published extensively in various international journals of atmospheric sciences and served as an editor of the Journal of Atmospheric Sciences.

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    Praise for this book

    ‘Professor Mak’s new text provides a comprehensive and self-contained introduction to atmospheric dynamics. The latter chapters provide invaluable material on a range of topics not found together in other texts: baroclinic lifecycles, the dynamics of stationary waves, and moist baroclinic instability. It presents a forceful case for the ability of dynamical analysis to continue to clarify the atmosphere’s behavior.’ Dr Daniel Kirk-Davidoff, Department of Meteorology, University of Maryland

    ‘This book is a thoughtful distillation of decades of teaching. It includes figures from illustrative computations that are custom-fitted to the mathematical development. Although it is brisk and condensed, with so much material to cover, the book has a clear and distinctive voice, and offers some unique treatments and insights.’ Dr Brian Mapes, Rosenstiel School of Marine and Atmospheric Science, University of Miami

    ‘This text neatly and logically outlines atmospheric dynamics, from the fundamental concepts in Chapter 1 and the development of the primitive equations in Chapter 2 to wave dynamics in Chapter 5 and overturning circulations in Chapter 10. All the while, walking the reader through the derivations and theory, yet referencing the physical applications with maps and diagrams or model outputs. It would be a helpful reference for any graduate student or scientist. Mak’s text would quickly educate someone new to atmospheric science, but ready to jump in to the fray at the graduate level. … It really is a nicely written text.’ Dr Teresa Bals-Elsholz, Department of Geography and Meteorology, Valparaiso University

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    Atmospheric Dynamics

    MANKIN MAK University of Illinois at Urbana-Champaign

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    cambridge university press

    Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Dubai, Tokyo, Mexico City

    Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK

    Published in the United States of America by Cambridge University Press, New York

    www.cambridge.org Information on this title: www.cambridge.org/9780521195737

    # Mankin Mak 2011

    This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements,

    no reproduction of any part may take place without the written permission of Cambridge University Press.

    First published 2011

    Printed in the United Kingdom at the University Press, Cambridge

    A catalog record for this publication is available from the British Library

    Library of Congress Cataloging-in-Publication Data

    Mak, Mankin, 1939– Atmospheric dynamics / Mankin Mak.

    p. cm. ISBN 978-0-521-19573-7 (Hardback)

    1. Atmospheric physics–Textbooks. 2. Meteorology–Textbooks. I. Title. QC861.3.M335 2011

    551.5105–dc22 2010029996

    ISBN 978-0-521-19573-7 Hardback

    Additional resources for this publication at www.cambridge.org/9780521195737

    Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to

    in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

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    To the memory of my parents who made it possible for me to pursue my dreams

    v

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    Contents

    Preface page xi

    1 Fundamental concepts and physical laws 1 1.1 Basic notions 1 1.2 Laws of mechanics 3 1.3 Equations of motion in a rotating reference frame 5 1.4 Forces 14 1.5 Conservation of mass 17 1.6 Thermodynamics and equation of state 19 1.7 Stratification and baroclinicity 23 1.8 Summary of the equations for a dry atmospheric model 25

    2 Basic approximations and elementary flows 27 2.1 Sphericity of the Earth and thin-atmosphere approximation 27 2.2 Hydrostatic balance, implications and applications 28 2.3 Geostrophic balance 38 2.4 Thermal wind relation 40 2.5 Balanced flows 41 2.6 Kinematic properties of wind 49 2.7 Divergent wind and vertical motion 53 2.8 Summary: z-, p- and y-coordinates and equations of balance 54

    3 Vorticity and potential vorticity dynamics 55 3.1 Vorticity and circulation of a three-dimensional flow 55 3.2 Relationship between vorticity and circulation 57 3.3 Kelvin circulation theorem 60 3.4 Dynamics of sea-breeze from the circulation perspective 61 3.5 Tendency of relative circulation 63 3.6 General vorticity equation 64 3.7 Vorticity dynamics